Challah, Chapter 1, Mishnah 4. The previous mishnah listed items that were exempt from ma'aser yet obligated in challah; our mishnah deals with precisely the opposite case. The wording of the mishnah: "Eilu chayavin b'ma'asros u'peturin min hachallah" - these are obligated in ma'asros, meaning they are obligated in ma'asros and in terumas ma'aser, but exempt from the obligation of challah.
Species that are not among the five grains:
The mishnah begins by listing species that are not considered grain, and since they are not among the five grains they cannot become chametz. As has already been explained in this tractate, there is no obligation of challah except in something that can become chametz. And these are they:
"Ha'orez" - rice.
"Vehadochan" - millet.
"Vehaparagim" - poppy seeds.
"Vehashumshemin" - sesame seeds.
"Vehakitniyos" - legumes.
The measure that creates the obligation:
Having finished dealing with the various species, the mishnah turns to the required measure: "Ufachos meichamishah reva'im b'tevuah" - less than five quarters of grain. Even when we are dealing with grain from the five species that are obligated in challah, if the quantity of flour is less than five quarters there is no obligation of challah. This is the measure for challah, which amounts to forty three eggs and a fifth of an egg. With less than that there is no obligation of challah, though of course the obligation of ma'aser remains.
Doughs that are not made in the ordinary way:
"Hasufganin" - baked goods whose texture resembles a batter rather than a dough, and therefore they are exempt.
"Vehadevshanin" - dough fried in honey, or kneaded with honey.
"Veha'iskritin" - another food that is based on a batter.
"Vechalas hamasres" - a thick dough, except that it is cooked in water. Since it will ultimately be cooked in water, it is not obligated in challah.
The meduma:
"Vehamduma" - grain or flour into which Terumah became mixed. All of these are exempt from challah. It is worth noting an interesting point: in a mixture of this kind the majority is unconsecrated produce, and by strict law the Terumah should have been nullified by the majority on a Torah level, with only a rabbinic requirement of one part in a hundred in order to nullify it.
For this reason, some commentators explain that this case must be dealing specifically with challah in our times, whose obligation is rabbinic. For by Torah law there is no genuine mixture of Terumah here, and the dough should have been obligated in challah. But since we are in any case dealing with a rabbinic challah, we can say that since the Sages ruled that the Terumah is not nullified under these circumstances, the dough is no longer considered obligated in challah.
In summary: This mishnah lists those items that are exempt from challah yet obligated in ma'asros: species that are not among the five grains and cannot become chametz (rice, millet, poppy, sesame and legumes), a dough that does not contain the measure of five quarters, doughs that are not made in the ordinary way (sufganin, devshanin, iskritin and chalas hamasres), and the meduma, whose exemption was explained on the basis of the rabbinic obligation of challah in our times.